The concept that scientists and engineers should be able to monitor and control simulations running on supercomputers has been discussed and implemented since the late 1980s. The recent explosion in the variety and capabilities of mobile devices allows this access to be taken to a new level, since the simulations running on supercomputers can be accessed as users are moving around in their normal work activities. This means that they have to be able to connect and disconnect at will from the simulation running on the supercomputer, without disturbing its execution. We present a general framework for such 'mobile supercomputing' within the framework of Web services standards. To illustrate the potential of our method, we present a particular application of this framework to provide a rich mobile interface to a lattice-Boltzmann simulation of complex fluids running on an IBM Blue Gene/Q supercomputer. © 2014 IEEE.